1. Field of the Invention
The invention relates generally to exploring for hydrocarbons using electrical investigation. More particularly, the invention relates to a method and apparatus for discriminating against unwanted signals that are dephased from the desired signal.
2. Background Art
When exploring a borehole drilled through an earth formation, it is desirable to know the characteristics of the geologic formation at various depths of the borehole. These characteristics include the stratifications, non-homogenous elements, and the size and shape of pores and breaks in the formation.
One technique for detecting these characteristics uses a tool with a series of current electrodes located on the face of a conductive pad that is pressed against the wall of the borehole. A constant current source injects a measurement current into the formation through a source electrode and returns the current through a return electrode situated on another part of the pad. The pad is moved along the borehole wall, and the discrete current signals associated with each electrode are related to the resistivity of the formation. If, however, a non-conductive drilling fluid (“mud”) is used, such as an oil based mud or water-in-oil emulsion type mud, the resulting non-conductive mud layer between the pad and the wellbore wall produces poor and unusable signals.
Another technique can image a borehole drilled with a non-conductive mud. The tool for this technique uses a non-conductive pad with two current injectors and an array of voltage electrodes. The two current injectors, a source electrode and a return electrode, inject a current into the formation, and the current passes through the formation in a path parallel to the pad. The voltage electrodes measure the voltage differential in the formation where the current is passing. This measurement of the voltage is important because the resistivity of the formation is related to the voltage.
The resistivity of the formation can be calculated using the following equation:
                    ρ        =                  E          J                                    (        1        )            where ρ is the resistivity of the formation, E is the electric field in the formation, and J is the current density. The electric field E is given by the differential voltage δV divided by the voltage electrode separation, and the current density J is given by the current I divided by a geometric factor g. Substituting for E and J in Equation 1 gives:
                    ρ        =                  k          ⁢                                                                                ⁢                              δ                ⁢                                                                  ⁢                V                                      I                                              (        2        )            where k is a geometric factor with units of length. Thus, the resistivity of a formation can be determined by injecting a current into the formation, measuring a voltage, and computing the resistivity of the formation using Equation 2.
The prior art pad used in this method is shown in FIGS. 1A and 1B. The pad is shown generally in FIG. 1 at element 1. It contains a source electrode 2, a return electrode 3, and an array of pairs of voltage electrodes 4. The pad 1 itself is constructed of a non-conductive, insulative material 5, such as ceramics or polymers, that have a high strength, and high chemical and thermal stability.
The pad 1 is placed against the wall of a borehole 7, which may have a mud cake layer 6. An electrical current is injected into the formation 8 through the source electrode 2, returning at the return electrode 3. The voltage electrodes 4 measure a voltage in the formation 8, and the resistivity of the formation can be calculated using Equation 2, above.
When the pad 1 is not in contact with the borehole wall 7, the distance between the pad 1 and the borehole wall 7 is called “standoff.” There are three main standoff effects: (1) mud and pad signals, (2) current leakage, and (3) voltage inaccuracies. There are various ways to reduce these effects so that accurate measurements can be made even when the pad 1 is not in direct contact with the borehole wall 7.
The current electrodes 2, 3 generate an electric field in the mud and in the insulating pad 5 which is detected by the voltage electrodes 4. One tool to reduce pad signal, shown in FIG. 9B, has a conductive backplate 92 behind the insulating pad 5 and parallel to the front face of the tool 1. The backplate 92 is maintained at an electrical potential equal to that of the formation in front of the voltage electrodes 4. This technique is described in Patent WO 0177711. This shields the array of voltage electrodes from the mud and pad signals.
“Current leakage” describes the condition when not all of the current injected from the source electrode 2 passes through the formation 8, referring to FIG. 1A. Ideally, when the pad 1 makes good contact with the borehole wall 7, the injected current passes almost entirely through the formation 8. But when mud or a mud cake layer 6 lies under one or both current electrodes 2, 3, when there is significant standoff, part of the current, called leakage current, will leak by capacitive coupling from the source electrode 2 to the return electrode 3, without passing through the formation 8. This situation is shown in the model circuit in FIG. 2.
FIG. 2 shows a current source 21 modeled to be in a parallel circuit with a leakage impedance ZL and a variable mud impedance ZM. The formation current IF passes through the impedance of the mud or mud cake layer and through the formation. The leakage current IL passes through the leakage impedance ZL, but does not pass through the formation. When calculating the resistivity of the formation, the formation current must be used in Equation 2.
The leakage current IL and the formation current IF sum to the total current I. Thus, the formation current is given by:IF=I−IL  (3)Using Z=(V/I), the above equation can be transformed into a more useful form:
                              I          F                =                  I          ⁡                      [                          1              -                                                Z                  INJ                                                  Z                  L                                                      ]                                              (        4        )            where ZINJ is the total impedance seen by the injector circuit, as measured by the tool, and ZL is the leakage impedance of the tool, which can be experimentally determined. Thus, the formation current IF can be computed from the injection voltage and current, without knowing the formation impedance ZF, standoff, or mud properties. An alternative method for determining the true current in the formation is to use injection electrodes 2,3 that are shielded by a conductive box, where the shields are maintained at the same electric potential as each electrode, as described in Patent WO 0177710.
Errors in the voltage measurement occur because the voltage electrodes 4 couple not only to the formation but also to the conductive backplate. The voltage output from the electrodes is given by:
                              δ          ⁢                                          ⁢          V                =                  δ          ⁢                                          ⁢                      V            TRUE                    ⁢                                    Z              S                                                      Z                S                            +                              Z                C                                                                        (        5        )            where δVTRUE is the true voltage in the formation, ZS is the coupling impedance to the backplate and ZC is the contact impedance between the voltage electrodes and the formation. A scalar correction is obtained by solving for δVTRUE:
                              δ          ⁢                                          ⁢                      V            TRUE                          =                  δ          ⁢                                          ⁢                      V            ⁡                          (                              1                +                                                      Z                    C                                                        Z                    S                                                              )                                                          (        6        )            
FIG. 4 is a diagram of an equivalent circuit showing the current flow using the prior art tool. It is similar to FIG. 2, but shows more detail along the path of the formation current IF. FIG. 4 shows the mud impedance ZM of FIG. 2 to be a series containing a mud impedance at the upper or source electrode ZMU, a formation resistance RF, and a mud impedance at the lower or return electrode ZML. Thus, the formation current flows through the formation resistance RF via the two mud impedances ZMU, ZML.
To a first approximation, the contact impedance of a voltage electrode ZC is linearly proportional to the mean contact impedance of the current injection electrodes:
                              Z          C                =                              (                                                            Z                  MU                                +                                  Z                  ML                                            2                        )                    ·                      (                                          A                INJ                                            A                BUT                                      )                                              (        7        )            where AINJ is the current injector 2, 3 area and Abut is the voltage electrode 4 (button) area.
Because the mud impedances under the injectors ZMU, ZML are usually much greater than the impedance of the formation RF, V=IR can be rewritten as:
                                          Z            MU                    +                      Z            ML                          ≈                  V                      I            F                                              (        8        )            where IF is given by Equation 4 and V is the voltage difference across the current electrodes 2, 3. Thus, δVTRUE can be calculated from V and I without knowing the standoff or mud properties.
FIGS. 3A and 3B show experimental resistivity data. FIG. 3A shows raw, uncorrected data in two different mud types, a 90/10 oil to water ratio mud and a 50/50 ratio mud, and with two different formations of mown resistivity, 20 Ω-m and 200 Ω-m Data with a conductive steel casing are also shown. The casing data lines represent the signal in the mud and shows how the mud signal affects the measured resistivity as the standoff increases. At large standoffs, the measured signal is composed almost entirely of the mud signal and not the formation signal. FIG. 3B shows the resistivity data after applying the scalar correction in Equations 4 and 6. The scalar corrected resistivity curves in the two formations are more accurate in the range from no standoff to the point on each curve where the mud signal becomes dominant, but at large standoff the mud signal overwhelms the formation signal and the data are unusable.